As long as it meets the voltage/power ratings, you can power it with whatever you like.
A transformer by itself is not a "power supply", an SMPS uses a transformer too, just at a higher frequency which makes it more efficient/smaller. What they are referring to on the DIY Audio forums is a "linear supply", which is more basic but easier to make less noisy than an SPMS so often used for audio. Ratings work the same for either type.
An SMPS can come with whatever voltage outputs you desire, there are plenty of dual rail (positive and negative) supplies out there.
If the SMPS is a good quality and quiet (check datasheet) then there is no reason you can't use it to power your amp.
The TDA7293 can supply up to 100W into 8 ohm. These boards specify 85W however so stick with that rating (or below). To find out the average current needed into 8 ohms for this wattage, the formula is sqrt(W/R) = sqrt(85/8) = 3.26A. The amplifier is not 100% efficient though so you need a higher input wattage to reach this level of output.
What supply depends on how hard you want to drive the boards, but something like they recommend is a good idea, e.g. +/- 30V 150W supply.